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Abstract

Connections between classification and lumpability in the stochastic Hopfield model (SHM) are explored and developed. A simplification of the SHM's complexity based upon its inherent lumpability is derived. Contributions resulting from this reduction in complexity include: (i) computationally feasible classification time computations (ii) a development of techniques for enumerating the stationary distribution of the SHM's energy function and (iii) a characterization of the set of possible absorbing states of the Markov chain associated with the zero temperature SHM.